Alili, Larbi and Chaumont, Loïc (2001) A new fluctuation identity for Lévy processes and some applications. Bernoulli, Volume 7 (Number 3). pp. 557-569. ISSN 1350-7265.

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Abstract

Let τ and H be respectively the ladder time and ladder height processes associated with a given Lévy process X. We give an identity in law between (τ,H) and (X,H*), H* being the right-continuous inverse of the process H. This allows us to obtain a relationship between the entrance law of X and the entrance law of the excursion measure away from 0 of the reflected process (Xt- infs≤tXs, t ≥0). In the stable case, some explicit calculations are provided. These results also lead to an explicit form of the entrance law of the Lévy process conditioned to stay positive.

Item Type:	Journal Article
Divisions:	Faculty of Science, Engineering and Medicine > Science > Statistics
Journal or Publication Title:	Bernoulli
Publisher:	Int Statistical Institute
ISSN:	1350-7265
Official Date:	2001
Dates:	Date Event 2001 Published
Volume:	Volume 7
Number:	Number 3
Number of Pages:	12
Page Range:	pp. 557-569
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Open Access (Creative Commons)
Date of first compliant deposit:	28 July 2016
Date of first compliant Open Access:	28 July 2016

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